Damage functions for transport infrastructure

Purpose – Damage functions constitute an essential part of the modelling of critical infrastructure (CI) performance under the influence of climate events. This paper aims to compile and discuss publications comprising damage functions for transport assets. Design/methodology/approach – The research included the collection of contemplable literature and the subsequent screening for damage functions and information on them. In conclusion, the derived damage curves and formulae were transferred to a unified design. Findings – Damage functions for the transport sector are scarce in the literature. Although specific damage functions for particular transport assets exist, they mainly consider infrastructure or transport in general. Occasionally, damage curves for the same asset in different publications vary. Major research gaps persist in wildfire damage estimation. Research limitations/implications – The study scope was restricted to the hazards of fluvial floods andwildfires. Despite all efforts, this study did not cover all existing literature on the topic. Originality/value – This publication summarises the state of the art of research concerning transport asset damage functions, and hence contributes to the facilitation of prospective research on CI performance, resilience and vulnerability modelling.


Introduction
Climate change and its consequences are currently in broad discussion. "Observational evidence from all continents and most oceans shows that many natural systems are being affected by regional climate changes" (IPCC, 2007). Field et al. (2012) expected extensive effects on infrastructure from climate events. This is where research gaps emerged. According to Mehrotra et al. (2011), these involved research on quantifying expected climate impacts on transport networks and users: Infrastructure is an understudied area of direct tangible damage. Many studies have ignored it altogether, although evidence indicates that damage to infrastructure can constitute a large proportion of the overall damage total . required a characterisation of the connections between hazards and losses. Damage functions depict the said correlation, and thereby constitute an essential part of the modelling. This literature review collected and discussed existing damage functions for transport assets, with the objective to facilitate future research in interconnected CI performance modelling. The paper introduces the EU-CIRCLE project, which this research affiliates to. Further, it defines the terminology of CI damage assessment, provides an overview of relevant literature and displays exemplary curves for specific assets.

The EU-CIRCLE project
This research is affiliated to the pan-European project EU-CIRCLE. The project obtained funding by the European Commission DG -Connect in the Horizon 2020 Framework Programme in the period 2015-2018: The central part of the research was the modelling of CI behaviour affected by natural hazard events, regarding the interdependencies within linked CI networks. The modelling of hazard-induced damages and losses utilised damage functions as input. Various functions from the literature were selected to characterise the behaviour of assets appendant to different infrastructure sectors.
The modelling results were implemented in five case studies: (1) electrical grid and highways affected by extreme droughts and forest fires, South France; (2) electrical grid disruption due to forest fires, Cyprus; (3) impacts from coastal floods on roads, railways and buildings, the UK; (4) cyclone impacts on electrical grid, Bangladesh; and (5) sewage and electricity disruption due to fluvial floods, Germany.
The multiplicity of transport assets required the selection of an asset sample regarding the relevance for the case studies, to conduct the case study modelling within the project timeframe. The comparison of the modelling results with real historic data of similar incidents allowed the calibration of the modelling and the applied damage functions. The developed EU-CIRCLE framework enables modellers to conduct the modelling for multihazard events and interconnected networks of different CI sectors.

Research methodology
The research took place as a secondary research. The majority of publications were in English language. In addition, the collection included papers in German and Dutch from publication references. Further publications found in the reference lists of papers augmented the sample. The literature collection contained 327 papers in total. The screening process involved three rounds (confer Figure 1). The terms of reference were pertinent to EU-CIRCLE case studies 1 and 5, confining the regarded hazards to wildfire and fluvial floods. In total, 166 papers were discarded in the first round. About 106 publications did not pass the second screening for information on damage functions. Finally, 29 papers remained after the third screening, as they contained damage curves utilisable for the modelling of transport infrastructure affected by flood or wildfire. Transferring the damage functions from the literature into a unified design ensured comparability and avoided biases. Terminology and definitions Critical infrastructure Country governments worldwide defined the term "critical infrastructure" differently. The German Federal Ministry of the Interior (2008) defined CI: [. . .] as organizations and institutions of central importance for the country and its people whose failure or functional impairment would lead to severe supply bottlenecks, significant disruption of public security or other dramatic consequences.
The US Government referred to: [. . .] systems and assets, whether physical or virtual, so vital to the United States that the incapacity or destruction of such systems and assets would have a debilitating impact on security, national economic security, national public health or safety, or any combination of those matters (Francis and Bekera, 2014). Johansson and Hassel (2010) and Larsen et al. (2008) provided and discussed further definitions.

Damage
Defining damage, Vanneuville et al. (2005) referred to material losses consequent on hazardous events. In the literature, a high consensus according to the differentiation of damage categories was discernible (see Figure 2)  Recent publications attempted to assess operational damages (Thieken et al., 2016). "Many case studies have applied a percentage of direct damage as representative of the indirect damage [. . .], which is a rather coarse assumption" (Olesen et al., 2017). Taylor et al. (2006) and Matsushima et al. (2007) approached the inclusion of inconveniences and losses from reduced road network accessibility. Difficulties appeared in the monetisation of intangible damages. The assessment of direct damages necessitated the monetary estimation of asset values . These describe the maximum damage "for a virtual scenario in which everything is destroyed" (Deckers et al., 2010). The literature research revealed two options for maximum damage determination (Albano et al., 2015;Merz et al., 2010): (1) replacement costs; and (2) depreciated/repair costs.
Replacement costs tended to overestimate damages, because they included infrastructure improvements after restoration . Penning-Rowsell et al. (1) Empirical approaches: "use damage data collected after flood events" (Merz et al., 2010).
Surveys with large samples were conducted for the collection of information on property types, hazard severity and damages. A subsequent regression analysis revealed typical depth damage functions for different assets (Messner et al., 2007).
Synthetic assessment approaches examined standardised assets (Messner et al., 2006). The synthetic functions were calibrated in consideration of real recorded damages. Figure 4 summarises the advantages and disadvantages of both approaches. Design criteria further influence the resilience of CI assets. "Agency policy and standards generally define the design event based on consideration of the nature of the structure, the roadway, or of the transportation facility served" (Federal Highway Administration, 2016). Albano et al. (2015) identified uncertainties of damage functions due to insufficient data and simplifications in the modelling. Scorzini and Leopardi (2017), Moel and Aerts (2011) and Bubeck et al. (2011) compared several damage models and discovered large deviations between them. Notaro et al. (2014) examined the influences of different damage functions by applying them to the same area. According to Messner and Meyer (2005), uncertainties emerged due to the omission of indirect effects. A profound examination of uncertainties was provided by Wagenaar et al. (2016).
In the literature, produced damage functions were mostly based on historic event data, which made them less suitable for different areas. To find damage functions that best represent the considered area, Wagenaar et al.  Tables I and II contain the publications providing information on damage functions, hazard-damage relations and damage functions themselves for transport assets. These papers passed screening rounds 2 and 3.

Infrastructure in general
The majority of damage functions in the literature addressed infrastructure in general. Meyer and Messner (2005)  Various references contained joint roads and railways damage functions. Figure 9 illustrates the damage function from Kok et al. (2004). Vanneuville et al. (2003) introduced a function (see Figure 8), which is also contained in Deckers et al. (2010), Vanneuville et al. (2005), Verwaest et al. (2008) and Kellens et al. (2013). Flood damage functions for roads and railways were the most consistent functions in the literature. , Pregnolato et al. (2017) and Jenelius and Mattsson (2015) approached the estimation of operational damages emerging from road closure (Figure 10).

Bridges
The research did not reveal damage functions for bridges. The Department of Homeland Security FEMA (2013) emphasised a low probability of bridge failure due to flooding, because design standards required resilience to standardised flood events. The structural damage of bridges depends on bridge type, technical equipment, structural features and position in the infrastructure network. Mostafaei et al. (2014) examined fire damage to bridges based on reported incidents. They concluded that a collapse, equivalent to total damage, occurred after short fire duration when the bridge was directly affected. Alutaibi (2017) assumed that "the level of damage is influenced by several factors such as wind speed and direction, and fuel type and load".   Chen et al. (2010) Impacts of high temperatures on asphalt Chen et al. (2015) Course of functions  Function estimation, variables Hardy (2005) Indicators/variables for fire damage International Joint Commission (2000) Function estimation, formula for CI damages Jofré et al. (2010) Behaviour of asphalt and concrete in fire Mattsson and Jenelius (2015) Schematic damage function Merz et al. (2010) Function estimation, approach discussion Mostafaei et al. (2014), Pool (2016), Wright et al. (2013) Structural damage to bridges due to fire Lee and Kim (2018) Schematic function for precipitation Penning-Rowsell et al. (2005) Operational damages Prahl (2016), Prahl et al. (2016) Adaption of functions Pregnolato et al. (2017) Formulae for operational damages on roads Reese and Ramsay (2010) Flood impacts on roads US Department of Agriculture (2013) Schematic of wildfire damage functions; indirect, intangible losses IJDRBE 9,4/5 Gasoline stations and train stations Vanneuville et al. (2006) developed flood damage functions for industry (see Figure 9), which the authors applied to gasoline stations, airports and train stations, disregarding the structural and operational differences between these assets. Damage curves for indirect or intangible losses were unavailable. The research also did not reveal damage functions for wildfire damages.
Airports Kok et al. (2004) developed a flood damage function for airports ( Figure 11). Vanneuville et al. (2006) also applied the damage function for industry (see Figure 12). Both curves  (2010) Flood damage for mobile and immobile traffic and infrastructure Deckers et al. (2010): Flood damage for roads and railways  Formulae for system and disruption losses of infrastructure, marginal costs and delay costs due to flood  Flood damage for infrastructure: system damage, disruption loss, marginal and delay Genovese (2006) Flood damage for infrastructure Gönnert et al. (2004): Flood damage for trade and traffic  Flood damage for transport and transport services; formulae for velocity attenuation; for economic losses of fuel consumption, time consumption of private cars and motor coaches Huizinga et al. (2017) Flood damage for roads in Europe ICPR (2001,2016) Formula for flood damage to mobile and immobile traffic Kellens et al. (2013) Flood damage for roads Kellermann et al. (2015) Flood damage for mobile and immobile traffic and infrastructure Klijn et al. (2007) Flood damage for infrastructure Kok et al. (2004) Flood damage for airports, roads and railways Messner and Meyer (2005) Flood damage for traffic þ telecommunications Meyer and Messner (2005) Formula for flood damage to immobile traffic Mittelstädt Flood damage for traffic and communication Norwegian Geotechnical Institute (2014) Flood damage for roads and bridges Aerts (2011), Penning-Rowsell et al. (2013) Formula for flood damage to immobile traffic Evacuation travel cost, flood damage for roads and railways Tariq et al. (2013) Flood damage for roads van der Sande et al. (2003) Flood damage for roads van der Sande (2001) Flood damage for roads Vanneuville et al. (2003Vanneuville et al. ( , 2005 Flood damage for roads and railways Vanneuville et al. (2006) Flood damage for gasoline stations, train stations and airports Verwaest et al. (2008) Flood damage for roads and railways  Kok et al. (2004) showed a fast damage growth reaching maximum damage at 3.5 m inundation depth. Functions for indirect or intangible damages were non-existent. The review did not reveal damage functions for wildfire damages.

Conclusions
The literature screening revealed several publications comprising damage functions for transport assets. Precedent publications contained several damage functions for infrastructure in general. However, profound information on included assets was rarely available, whereby the application of general functions for the modelling at asset level ought to be considered carefully. Several insurance organisations possessed knowledge on damage estimations for CI. However, this knowledge was mostly proprietary and inaccessible.
Mentionable was the lack of consistent approaches to estimate wildfire severity. The review results corroborated the conclusion in Howard (2014) that most literature estimated particular fires or group of fires and lack generality. Further research on the estimation of losses from wildfire needs to broaden the existent investigations on the factors that influence fire damage. Inundation depth was the most frequently applied variable for flood severity. Although Merz et al. (2010) confirmed the multiplicity of influencing variables, they found no ample approach for including them in damage modelling. Messner and Meyer (2005) considered these variables as often disregarded due to their correlation with inundation depth. The literature review confirmed the need to include different hazard variables, as done by Kreibich et al. (2009). Lately, research started to pay particular attention to damages from Damage functions pluvial flooding, which still appeared to be sparsely examined (Vanneuville et al., 2016;Weerasinghe et al., 2018;Lee and Kim, 2018;Melvin et al., 2017).
More thorough research needs to take more assets and hazards into account. Furthermore, research gaps remained concerning interdependent infrastructure systems and their performance in multi-hazard events. With lack of monitoring and management, they introduce new risks and societal consequences (Kaewunruen et al., 2016). Moreover, approaches for the estimation of cascading effects in interconnected transport infrastructure (Wang et al., 2018;Ouyang, 2014;Setola and Geretshuber, 2009;Trucco et al., 2012;Huang et al., 2014;Laugé et al., 2015;Dudenhoefer et al., 2006) need more profound examination. Existent damage estimation approaches primarily assessed direct damages. Indirect and intangible damages were often addressed, but not further estimated, mostly due to lack of data or knowledge. As the assessment of indirect and intangible damages came into focus, methodologies for their measurement need further development.
This literature review summarised the current state of the art in flood and fire damage estimation for transport assets. It gleaned damage curves scattered in various publications into an overview. The research results aimed to encourage and facilitate further damage estimations and CI network modelling. The development of frameworks for the modelling at the asset level as in the EU-CIRCLE project is important for flood damage forecasting and the enhancement of transport asset resilience, as well as the safety for network users.